my challenge problem - - - equation solving

[lookagain]

Solve for all real values of x:

(x - 1)(x - 2)(x - 3)(x - 5)(x - 6)(x - 7) = 650




Note: There is no (x - 4) factor on the left-hand side on purpose.


You may find the information helpful in my post (the third post in the thread in the below link) for a possible strategy:



http://www.freemathhelp.com/forum/threads/82409-help-poly

 

[Deleted member 4993]

Solve for all real values of x:

(x - 1)(x - 2)(x - 3)(x - 5)(x - 6)(x - 7) = 650

Note: There is no (x - 4) factor on the left-hand side on purpose.

You may find the information helpful in my post (the third post in the thread in the below link) for a possible strategy:

http://www.freemathhelp.com/forum/threads/82409-help-poly

By invoking Newton x₁ = 0.258342613 and x₂ = 7.741657387

 

[lookagain]

By invoking Newton x₁ = 0.258342613 and x₂ = 7.741657387

Please solve for exact answers. \(\displaystyle \ \ \ \) Hint: There are square roots as part of the real solutions.

 

[Bob Brown MSEE]

(a-9)(a-4)(a-1)=650 when a=14 (only real solution)

Let bb = 14 when symmetric about b=0
But p(x) is symmetric about x=4
x₁ = 4 - Root 14
x₂ = 4 + Root 14

 

[lookagain]

(a-9)(a-4)(a-1)=650 when a=14 (only real solution) You need to state what the relationship is between the variables a and x. *

Let bb = 14 when symmetric about b=0
But p(x) is symmetric about x=4
x₁ = 4 - Root 14
x₂ = 4 + Root 14

* For the conversion, \(\displaystyle \ x = \sqrt{a} + 4 \ \) is substituted for every x in the original equation.